JEE MATHEMATICS MCQ: QUADRATIC EQUATIONS

1 Easy

1 of 1

Application +4 | -1

If one root of the quadratic equation

a{x^2} + bx + c = 0

is equal to nth power of the other root, then the value of

{\left( {a{c^n}} \right)^{1/\left( {n + 1} \right)}} + {\left( {{a^n}c} \right)^{1/\left( {n + 1} \right)}}

is equal to

View answer and explanation

Correct option: B

- b

Option B (

-b

) is correct because it is the result of eliminating α from the sum and product of the roots, and then simplifying the expression.

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{x^2} - px + q = 0

{\alpha _1},{\beta _1}

{x^2} - qx + p = 0,

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{x^2} + 4ax + 2 > 0

x

a

f\left( x \right) = a{x^2} + bx + c\;

\;f\left( { - 1} \right) < 1,f\left( 1 \right) > - 1,f\left( 3 \right) < - 4\;

\;a \ne 0,

9{x^2} - 18\left| x \right| + 5 = 0

f\left( x \right) = \log \left( {{x^2} - x - 2} \right)